OF ECCENTRICITY AND GRADUATION. 



13 



can also be takeu from the Reclientafeln, by retainiug only the first 

 decimal place of sums containing more than three digits, which involves 

 a maximnm error ten-thirteenths of that referred to in connection with 

 the products in cohnnns 6 and 7 of Table I, and otherwise subject to the 



Table III. 



same conditions. Column 8 is expeditiously filled by laying the slip of 

 paper containing Table II upon the form, as before, and opening the 

 Rechentafeln at the value of A ; then opening at B, the products in col- 

 umn 9 are obtained with equal facility. 



The corrections for eccentricity appear in column 10, each term being 

 the sum of those on the same line in the two preceding columns ; these cor- 

 rections, with the further addition of X, are entered in column 11. After 

 subtracting the quantities in column 11 from the corresponding ones in 

 column 5 the residuals in column 12 remain ; their sum should not differ 

 from zero by more than two or three units. Finally the squares of the 

 residuals are entered in column 13, and the probable error of gradua- 

 tion and observation is computed from their sum by (9). The foregoing 

 formulas are equally applicable to any examination consisting of four- 

 teen comparisons at points ten degrees apart upon the arc of the sextant. 

 If it is preferred for any reason to make the comparisons elsewhere than 

 at 0°, 10°, etc., the eccentric corrections obtained for the points compared 

 may be rectified by subtracting from each of them the correction computed 

 for"/ = 0°. 



As a further illustration of what is to expected in practice, the eccen- 

 tric corrections, constants A and B, residuals, and probable errors, of six 

 sextants, by makers of high repute, are given in Table IV. 



